1. Field of the Invention
This invention relates to an interpolating operation method and apparatus for an image signal.
2. Description of the Prior Art
Techniques for photoelectrically reading out a radiation image, which has been recorded on a photographic film, in order to obtain an image signal, carrying out appropriate image processing on the image signal, and then reproducing a visible image by use of the processed image signal have heretofore been known in various fields.
Also, it has been proposed to use stimulable phosphors in radiation image recording and reproducing systems. Specifically, a radiation image of an object, such as a human body, is recorded on a sheet provided with a layer of the stimulable phosphor (hereinafter referred to as a stimulable phosphor sheet). The stimulable phosphor sheet, on which the radiation image has been stored, is then exposed to stimulating rays, such as a laser beam, which cause it to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation. The light emitted by the stimulable phosphor sheet, upon stimulation thereof, is photoelectrically detected and converted into an electric image signal. The image signal is then processed and used for the reproduction of the radiation image of the object as a visible image on a recording material, such as photographic material, or on a display device, such as a cathode ray tube (CRT) display device. Radiation image recording and reproducing systems, which use stimulable phosphor sheets, are advantageous over conventional radiography using silver halide photographic materials, in that images can be recorded even when the energy intensity of the radiation, to which the stimulable phosphor sheet is exposed, varies over a wide range.
In image recording and reproducing systems, in which an image signal is obtained in the manner described above and a visible is reproduced from the image signal, in cases where the region of interest in the visible image is to be viewed in more detail, the region of interest is often enlarged and reproduced. In such cases, in order for the enlarged image to be obtained, a predetermined interpolating operation may be carried out on the original image signal, which has been obtained by reading out an original image and is made up of a series of image signal components representing sampling points in the original image, and an interpolation image signal, which is a secondary image signal and is made up of a number of image signal components different from that of the original image signal, may thereby be formed. A visible image may then be reproduced from the interpolation image signal. In such cases, depending upon the image size enlargement scale factor, it often occurs that several interpolation points overlap upon the sampling points.
Ordinarily, as an aid in facilitating the constitution of image input and output devices, the sampling points (i.e., picture elements of the original image), which are represented by the image signal components of the original image signal, are arrayed at predetermined intervals along horizontal and vertical directions in a square lattice-like form, and an image is thereby formed. In such cases, as the interpolating operation in the image size enlargement processing, a linear interpolating operation is carried out on the original image signal components representing four sampling points located in the vicinity of an interpolation point, which is to be newly set from the interpolating operation, and an interpolated image signal component corresponding to the interpolation point is thereby obtained.
For example, as illustrated in FIG. 5A, picture elements S, S, . . . of an original image, which are indicated by the xe2x80x9coxe2x80x9d mark, may be arrayed in a square lattice-like form. Interpolated image signal components corresponding to interpolation points Sxe2x80x2, Sxe2x80x2, . . . , which are indicated by the xe2x80x9cxxe2x80x9d mark and are arrayed at intervals different from the intervals of the picture elements S, S, . . . , may then be obtained. In such cases, for example, the interpolated image signal component corresponding to an interpolation point Sxe2x80x20 is obtained in the manner described below.
In the calculation of the interpolated image signal component corresponding to the interpolation point Sxe2x80x20, image signal components SA, SB, SC, and SD representing four picture elements SA, SB, SC, and SD of the original image, which picture elements are located in the vicinity of the interpolation point Sxe2x80x20 so as to surround it (and which constitute the unit lattice constituting the square lattice), are used. (As an aid in facilitating the explanation, the same symbol as that of a picture element is used for the image signal component representing the picture element.) This means that a square mask of the unit lattice containing the interpolation point is set, and the image signal components representing the sampling points, which are located in the square mask, are used.
The pitch between the picture elements SA and SB, the pitch between the picture elements SC and SD, the pitch between the picture elements SA and SC, and the pitch between the picture elements SB and SD are respectively taken as being equal to 1. Also, as illustrated in FIG. 5B, the distance between the picture element SA (or SC) and the interpolation point Sxe2x80x20, the distance being taken along the x axis direction (i.e., the horizontal direction), is represented by Tx. The distance between the picture element SA (or SB) and the interpolation point Sxe2x80x20, the distance being taken along the y axis direction (i.e., the vertical direction), is represented by Ty. In such cases, interpolated image signal components Sm and Sn, which respectively correspond to interpolation points Sm and Sn, that correspond to the positions of the interpolation point Sxe2x80x20 taken respectively from the picture elements SA and SC along the x axis direction, are calculated with linear interpolating operations represented by Formulas (28) and (29) shown below.
Sm=(1xe2x88x92Tx)SA+TxSBxe2x80x83xe2x80x83(28)
Sn=(1xe2x88x92Tx)SC+TxSDxe2x80x83xe2x80x83(29)
Thereafter, a linear interpolating operation is carried out for the interpolation point Sxe2x80x20 and with respect to the y axis direction by using the interpolated image signal components Sm and Sn, and an interpolated image signal component Sxe2x80x20 is thereby calculated. The linear interpolating operation is represented by Formula (30) shown below.
Sxe2x80x20=(1xe2x88x92Ty)Sm+TySnxe2x80x83xe2x80x83(30)
The same operations as those described above are also carried out for the other interpolation points Sxe2x80x2, Sxe2x80x2, . . . , and the corresponding interpolated image signal components Sxe2x80x2, Sxe2x80x2, . . . can thereby be obtained.
The interpolation method described above is not limited to the use in cases where the image size is to be enlarged, and can be applied when the image size enlargement or reduction is not carried out. The interpolation method described above can also be applied when details of the image are to be reproduced appropriately, e.g., when a high-resolution image is to be reproduced.
Also, the sampling points, from which the interpolated image signal component is to be calculated, are not limited to the four sampling points located in the vicinity of the interpolation point. For example, sampling points located in a square mask, which comprises 4xc3x974 sampling points and contains the four sampling points located in the vicinity of the interpolation point, may be utilized.
For example, as in a radiation image containing bone patterns, a reproduced visible image ordinarily contains an image edge portion, at which the image density (or the luminance) changes sharply. It often occurs that the image edge portion is enlarged.
However, in cases where the picture elements of the original image are arrayed in the form of the square lattice (the unit lattice), it often occurs that the image edge portion extends in an oblique direction with respect to the square lattice. Also, in cases where the picture elements of the original image are arrayed in the form of a rhombic lattice, it often occurs that the image edge portion extends in the horizontal or vertical direction with respect to the rhombic lattice. In such cases, if the interpolating operations are carried out in accordance with Formulas (28), (29), and (30) shown above, step-like patterns will become perceptible at the enlarged image edge portion, which extends in the oblique direction with respect to the square lattice or in the horizontal or vertical direction with respect to the rhombic lattice.
For example, as illustrated in FIG. 7A, an image edge portion may extend in an oblique direction in an image. Microscopically, as illustrated in FIG. 7B, the boundary line (the image edge portion) between the region, in which points having a high image density (indicated by black dots) are located, and the region, in which points having a low image density (indicated by white dots) are located, may extend in the oblique direction in the image. In cases where an interpolated image signal component Sxe2x80x20 is calculated by applying the aforesaid interpolating operation to the image edge portion, the interpolated image signal component Sxe2x80x20 depends also upon an original image signal component SD representing the low image density. Therefore, as illustrated in FIG. 8B, an image signal component representing an intermediate image density slightly lower than the image density of the high-density picture elements SA, SB, and SC is obtained as the interpolated image signal component Sxe2x80x20. As a result, when the enlarged image is reproduced in accordance with the obtained interpolated image signal component Sxe2x80x20, the enlarged image is obtained in which the step-like pattern at the image edge portion has been enlarged as indicated by the broken line in FIG. 8B. Specifically, when the image size enlargement processing is carried out on the image edge portion, which extends in the oblique direction as shown in FIG. 7A, the step-like pattern at the image edge portion is enlarged as illustrated in FIG. 8A.
The enlarged step-like pattern at the image edge portion adversely affects the image quality in the region in the vicinity of the image edge portion. Therefore, there is the risk that an image capable of serving as an effective tool in, particularly, the efficient and accurate diagnosis of an illness, cannot be obtained.
The problems described above occur not only with an image, in which the sampling points are arrayed along horizontal and vertical directions in the square lattice-like form, but also with an image, in which an image edge portion extends in an oblique direction with respect to the array directions of the sampling points in a unit lattice, such as an image, in which the sampling points are arrayed along oblique directions in the form of a rhombic lattice and an image edge portion extends along the horizontal or vertical direction.
The problems described above occur when the interpolated image signal component corresponding to the interpolation point Sxe2x80x20 is calculated by using only the original image signal components SA, SB, SC, and SD representing the picture elements SA, SB, SC, and SD of the original image (four sampling points located in the vicinity of the interpolation point), which picture elements constitute the unit lattice containing the interpolation point. The same problems occur ordinarily when an interpolated image signal component corresponding to an interpolation point is calculated by using the image signal components representing the picture elements, which are located in a square mask containing the interpolation point.
As for image portions other than the image edge portion, i.e. as for a flat image density portion, at which the change in the image density is unsharp, and a portion inward from and surrounded by the image edge portion (these image portions will hereinbelow be referred to simply as the flat portion), it is desired that the sharpness of the flat portion in the reproduced visible image can be adjusted freely by the person, who views the image, such that a reproduced image having good image quality can be obtained.
The primary object of the present invention is to provide an interpolating operation method for an image signal, wherein interpolated image signal components corresponding to interpolation points, which are located at an image edge portion, and interpolation points, which are located at a flat portion, are obtained such that a visible image having good image quality can be reproduced from the interpolated image signal components and used as an effective tool in, particularly, the accurate and efficient diagnosis of an illness, i.e. such that a visible image, in which a character pattern and an image edge portion are free from any step-like pattern and are sharp and a flat portion has an appropriate level of sharpness, can be reproduced from the interpolated image signal components.
Another object of the present invention is to provide an apparatus for carrying out the interpolating operation method for an image signal.
An interpolating operation method for an image signal in accordance with the present invention is characterized by changing the interpolating operation process, depending upon whether an interpolation point is located at an image edge portion or at a flat image density portion, such that an interpolating operation process capable of obtaining a sharp image free from any step-like pattern may be applied with respect to the image edge portion, and such that an interpolating operation process capable of obtaining a smooth image or an interpolating operation process enabling sharpness to be adjusted may be applied with respect to the flat portion.
Specifically, the present invention provides an interpolating operation method for an image signal, wherein an interpolated image signal component corresponding to an interpolation point is calculated from original image signal components of an original image signal representing an original image, which represent a plurality of sampling points arrayed at predetermined intervals and in a lattice-like form, the method comprising the steps of:
i) making a judgment as to whether the interpolation point belongs to an image edge portion, at which the change in the original image signal is sharp, or belongs to a flat portion, at which the change in the original image signal is unsharp, and
ii) changing interpolating operation processes, one of which is to be employed for the interpolation point, over to each other in accordance with the results of the judgment.
In the interpolating operation method for an image signal in accordance with the present invention, the sampling points arrayed at predetermined intervals and in a lattice-like form. For example, the sampling points may be arrayed along horizontal and vertical directions and in a square lattice-like form or a rectangular lattice-like form. Alternatively, the sampling points may be arrayed along oblique directions and in a rhombic lattice-like form. Also, the lattice intervals may be kept the same for the two array directions or may be varied for the two array directions.
The judgment as to whether the interpolation point belongs to the image edge portion or the flat portion can be made by, for example, comparing the values of the original image signal components representing four sampling points, which constitute the unit lattice containing the interpolation point, with one another.
By way of example, as the interpolating operation process, which is employed in cases where, as a result of the judgment, it has been judged that the interpolation point belongs to the image edge portion, the interpolating operation process described in (1) or (2) below may be employed.
(1) An interpolating operation process comprising the steps of:
a) specifying the direction, along which the image edge portion extends, with respect to the array directions of the sampling points in a unit lattice, and
b) changing selection processes for selecting the original image signal components, from which the interpolated image signal component corresponding to the interpolation point is to be calculated, over to each other in accordance with the direction, along which the image edge portion extends.
(2) An interpolating operation process comprising the steps of:
a) calculating each of interpolation coefficients, by which the corresponding one of the original image signal components is to be multiplied, from the original image signal components, which represent a plurality of the sampling points located in the vicinity of the interpolation point,
b) calculating an image density gradient vector at the interpolation point on the original image, which is represented by the original image signal components,
c) calculating the distance between a line segment, which intersects perpendicularly to the image density gradient vector, and each of the sampling points located in the vicinity of the interpolation point,
d) correcting the interpolation coefficients such that the interpolation coefficient, by which the corresponding original image signal component is to be multiplied, may become small for a sampling point, for which the image density gradient vector and/or the distance is comparatively large, and
e) multiplying the original image signal component by the corresponding corrected interpolation coefficient.
In cases where the interpolating operation process described in (1) above is employed, the direction, along which the image edge portion extends, may be specified by, for example:
(a) grouping each of two sets of sampling points, each set being constituted of two sampling points, which are located at two diagonal positions facing each other in the unit lattice, that contains the interpolation point therein,
calculating the difference between the original image signal components representing the two sampling points, which constitute each of the two sets of sampling points, and
comparing the differences, which have been calculated for the two sets of sampling points, with each other; or
(b) grouping each of two sets of sampling points, each, set being constituted of two sampling points, which are located at two diagonal positions facing each other in the unit lattice, that contains the interpolation point therein,
calculating the difference between the original image signal components representing the two sampling points, which constitute each of the two sets of sampling points,
comparing the differences, which have been calculated for the two sets of sampling points, with each other, and
carrying out an operation in accordance with the original image signal components representing the sampling points, which are located around the unit lattice, that contains the interpolation point therein; or
(c) calculating an image density gradient vector with respect to each of the two array directions of the sampling points in the unit lattice, the calculation being made from the original image signal components representing four sampling points, which constitute the unit lattice, that contains the interpolation point therein, and
making a judgment from the magnitude and the product of the two image density gradient vectors, which have been calculated with respect to the two array directions of the sampling points in the unit lattice.
Also, in cases where the interpolating operation process described in (1) above is employed, the selection processes for selecting the original image signal components to be used in the calculation of the interpolated image signal component, the selection processes being changed over to each other in accordance with the direction, along which the image edge portion extends, may comprise, for example:
(i) a selection process, which is employed in cases where it has been specified that the image edge portion extends along an oblique direction with respect to the array directions of the sampling points in the unit lattice, the selection process comprising the steps of:
dividing the unit lattice into two triangular regions with the image edge portion serving as the boundary therebetween,
selecting a triangular region, which contains the interpolation point therein, from the two triangular regions, and
selecting the original image signal components, which represent the three sampling points, that constitute the triangular region containing the interpolation point therein, and
(ii) a selection process, which is employed in cases where it has been specified that the image edge portion extends along a direction parallel to one of the array directions of the sampling points in the unit lattice, the selection process comprising selecting the original image signal components, which represent the four sampling points, that constitute the unit lattice containing the interpolation point therein.
In cases where the interpolated image signal component corresponding to the interpolation point is calculated from the original image signal components representing the three sampling points, the interpolating operation may be carried out with one of various functions, such as a linear function, a second order function, and a higher order function.
The interpolating operation process, which is employed in cases where, as a result of the judgment, it has been judged that the interpolation point belongs to the flat portion, may be an interpolating operation process, with which the sharpness of the flat portion is rendered variable. By way of example, the interpolating operation process, with which the sharpness of the flat portion is rendered variable, may be:
(I) a spline interpolating operation process, or
(II) an interpolating operation process, comprising the steps of:
linearly combining interpolation coefficients Bij and Cij, which correspond to each other and are set for each of the original image signal components Yij, in two different interpolating functions f and g (for example, a cubic spline interpolating operation function and a B spline interpolating operation function) for obtaining two interpolation images having different levels of sharpness, which functions are represented by Formulas (24) and (25), the linear combination being carried out with Formula (26) by use of a variable factor xcex1, where xcex1 is set to be one of all real numbers, a new interpolation coefficient Aij being obtained from the linear combination, and
carrying out an interpolating operation on the original image signal components Yij by using an interpolating function h having the new interpolation coefficient Aij, which function is represented by Formula (27):
xe2x80x83f=xcexa3Bijxc2x7Yijxe2x80x83xe2x80x83(24)
g=xcexa3Cijxc2x7Yijxe2x80x83xe2x80x83(25)
Aij=(1xe2x88x92xcex1)Bij+xcex1Cijxe2x80x83xe2x80x83(26)
h=xcexa3Aijxc2x7Yijxe2x80x83xe2x80x83(27)
xe2x80x83in which i=1, 2, . . . , j=1, 2, . . . and
xcex1 represents one of all real numbers.
In cases where it has been judged that the interpolation point belongs to the flat portion, and the interpolating operation process, with which the sharpness of the flat portion is rendered variable, is employed, the interpolating operation process defined above for the image edge portion need not necessarily be carried out. Specifically, in cases where the interpolating operation process, with which the sharpness of the flat portion is rendered variable, is at least employed when it has been judged that the interpolation point belongs to the flat portion, any of conventional interpolating operation processes may be utilized as the interpolating operation process for the image edge portion.
As the spline interpolating operation process described in (I) above, by way of example, one of the interpolating operation processes described in (A), (B), and (C) below may be employed.
(A) The spline interpolating operation process is an interpolating operation process for obtaining an interpolated image signal component with Formula (1),
xe2x80x83Yp=akxe2x88x921Ykxe2x88x921+akYk+ak+1Yk+1+ak+2Yk+2xe2x80x83xe2x80x83(1)
in which Ykxe2x88x921, Yk, Yk+1, and Yk+2 represent the original image signal components representing sampling points serving as picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and akxe2x88x921, ak, ak+, and ak+2 represent the interpolation coefficients,
the process comprising the steps of:
a) calculating the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 respectively corresponding to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2 such that, in cases where the original image signal components representing the two picture elements Xkxe2x88x921 and Xk located before the interpolation point Xp, which is located between the picture elements Xk and Xk+1 in the original image, are represented by Ykxe2x88x921 and Yk, the original image signal components representing the two picture elements Xk+1 and Xk+2 located after the interpolation point Xp are represented by Yk+1 and Yk+2, a third-order spline interpolating function between the picture elements Xk and Xk+1 is represented by fk, a third-order spline interpolating function between the picture elements Xkxe2x88x921 and Xk is represented by fkxe2x88x921, and a third-order spline interpolating function between the picture elements Xk+1 and Xk+2 is represented by fk+1:
{circle around (1)} the spline interpolating function fk at the picture elements Xk and Xk+1 may satisfy the original image signal components Yk and Yk+1, as represented by Formulas (2) and (3):
fk(Xk)=Ykxe2x80x83xe2x80x83(2)
fk(Xk+1)=Yk+1xe2x80x83xe2x80x83(3)
{circle around (2)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fkxe2x88x921 at the picture element Xk, as represented by Formula (4):
fkxe2x80x2(Xk)=fkxe2x88x921xe2x80x2(Xk)xe2x80x83xe2x80x83(4)
{circle around (3)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5):
fkxe2x80x2(Xk+1)=fk+1xe2x80x2(Xk+1)xe2x80x83xe2x80x83(5)
{circle around (4)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may have an inclination of an arbitrary parameter xcex1 with respect to the gradient of the original image signal components Ykxe2x88x921 and Yk+1 representing the picture elements Xkxe2x88x921 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (6), the arbitrary parameter xcex1 being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation,
fkxe2x80x2(Xk)=xcex1(Yk+1xe2x88x92Ykxe2x88x921)/(Xk+1xe2x88x92Xkxe2x88x921)xe2x80x83xe2x80x83(6)
xe2x80x83and
{circle around (5)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may have an inclination of the parameter xcex1 with respect to the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (7):
fkxe2x80x2(Xk+1)=xcex1(Yk+2xe2x88x92Yk)/(Xk+2xe2x88x92Xk)xe2x80x83xe2x80x83(7)
xe2x80x83and
b) calculating the interpolated image signal component Yp corresponding to the interpolation point Xp in accordance with the calculated interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, and the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2.
(B) The spline interpolating operation process is an interpolating operation process for obtaining an interpolated image signal component with Formula (1),
Yp=akxe2x88x921Ykxe2x88x921+akYk+ak+1Yk+1+ak+2Yk+2xe2x80x83xe2x80x83(1)
in which Ykxe2x88x921, Yk, Yk+1, and Yk+2 represent the original image signal components representing sampling points serving as picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and akxe2x88x921, ak, ak+1, and ak+2 represent the interpolation coefficients,
the process comprising the steps of:
a) calculating the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 respectively corresponding to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2 such that, in cases where the original image signal components representing the two picture elements Xkxe2x88x921 and Xk located before the interpolation point Xp, which is located between the picture elements Xk and Xk+1 in the original image, are represented by Ykxe2x88x921 and Yk, the original image signal components representing the two picture elements Xk+1 and Xk+2 located after the interpolation point Xp are represented by Yk+1 and Yk+2, a third-order spline interpolating function between the picture elements Xk and Xk+1 is represented by fk, a third-order spline interpolating function between the picture elements Xkxe2x88x921 and Xk is represented by fkxe2x88x921, and a third-order spline interpolating function between the picture elements Xk+1 and Xk+2 is represented by fk+1:
{circle around (1)} the spline interpolating function fk at the picture elements Xk and Xk+1 may slightly deviate from the original image signal components Yk and Yk+1 in accordance with an arbitrary parameter xcex2, as represented by Formulas (12) and (13), the arbitrary parameter xcex2 being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation,
fk(Xk)=xe2x88x920.5xcex2Ykxe2x88x921+(1+xcex2)Ykxe2x88x920.5xcex2Yk+1xe2x80x83xe2x80x83(12)
fk(Xk+1)=xe2x88x920.5xcex2Yk+(1+xcex2)Yk+1xe2x88x920.5xcex2Yk+2xe2x80x83xe2x80x83(13)
{circle around (2)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fkxe2x88x921 at the picture element Xk, as represented by Formula (4):
fkxe2x80x2(Xk)=fkxe2x88x921xe2x80x2(Xk)xe2x80x83xe2x80x83(4)
{circle around (3)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5):
fkxe2x80x2(Xk+1)=fk+1xe2x80x2(Xk+1)xe2x80x83xe2x80x83(5)
{circle around (4)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the gradient of the original image signal components Ykxe2x88x921 and Yk+1 representing the picture elements Xkxe2x88x921 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (14):
xe2x80x83fkxe2x80x2(Xk)=(Yk+1xe2x88x92Ykxe2x88x921)/(Xk+1xe2x88x92Xkxe2x88x921)xe2x80x83xe2x80x83(14)
xe2x80x83and
{circle around (5)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (15):
fkxe2x80x2(Xk+1)=(Yk+2xe2x88x92Yk)/(Xk+2xe2x88x92Xk)xe2x80x83xe2x80x83(15)
xe2x80x83and
b) calculating the interpolated image signal component Yp corresponding to the interpolation point Xp in accordance with the calculated interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, and the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2.
(C) The spline interpolating operation process is an interpolating operation process for obtaining an interpolated image signal component with Formula (1),
Yp=akxe2x88x921Ykxe2x88x921+akYk+ak+1Yk+1+ak+2Yk+2xe2x80x83xe2x80x83(1)
in which Ykxe2x88x921, Yk, Yk+1, and Yk+2 represent the original image signal components representing sampling points serving as picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and akxe2x88x921, ak, ak+1, and ak+2 represent the interpolation coefficients,
the process comprising the steps of:
a) calculating the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 respectively corresponding to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+1 such that, in cases where the original image signal components representing the two picture elements Xkxe2x88x921, and Xk located before the interpolation point Xp, which is located between the picture elements Xk and Xk+1 in the original image, are represented by Ykxe2x88x921 and Yk, the original image signal components representing the two picture elements Xk+1 and Xk+2 located after the interpolation point Xp are represented by Yk+1 and Yk+2, a third-order spline interpolating function between the picture elements Xk and Xk+1 is represented by fk, a third-order spline interpolating function between the picture elements Xkxe2x88x921 and Xk is represented by fkxe2x88x921, and a third-order spline interpolating function between the picture elements Xk+1 and Xk+2 is represented by fk+1:
{circle around (1)} the spline interpolating function fk at the picture elements Xk and Xk+1 may satisfy the original image signal components Yk and Yk+1, as represented by Formulas (2) and (3):
fk(Xk)=Ykxe2x80x83xe2x80x83(2)
fk(Xk+1)=Yk+1xe2x80x83xe2x80x83(3)
{circle around (2)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fkxe2x88x921 at the picture element Xk, as represented by Formula (4):
fkxe2x80x2(Xk)=fkxe2x88x921xe2x80x2(Xk)xe2x80x83xe2x80x83(4)
{circle around (3)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5):
fkxe2x80x2(Xk+1)=fk+1xe2x80x2(Xk+1)xe2x80x83xe2x80x83(5)
{circle around (4)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may have an inclination of an arbitrary parameter xcex1 with respect to the gradient of the original image signal components Ykxe2x88x921 and Yk+1 representing the picture elements Xkxe2x88x921 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (6), the arbitrary parameter xcex1 being selected previously and determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation,
fkxe2x80x2(Xk)=xcex1(Yk+1xe2x88x92Ykxe2x88x921)/(Xk+1xe2x88x92Xkxe2x88x921)xe2x80x83xe2x80x83(6)
xe2x80x83and
{circle around (5)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may have an inclination of the parameter xcex1 with respect to the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (7):
fkxe2x80x2(Xk+1)=xcex1(Yk+2xe2x88x92Yk)/(Xk+2xe2x88x92Xk)xe2x80x83xe2x80x83(7)
b) calculating interpolation coefficients bkxe2x88x921, bk, bk+1, and bk+2 respectively corresponding to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2 such that:
{circle around (6)} the spline interpolating function fk at the picture elements Xk and Xk+1 may slightly deviate from the original image signal components Yk and Yk+1 in accordance with an arbitrary parameter xcex2, as represented by Formulas (12) and (13), the arbitrary parameter xcex2 being selected previously and determining the sharpness of the secondary image represented by the interpolation image signal obtained from the interpolating operation,
fk(Xk)=xe2x88x920.5xcex2Ykxe2x88x921+(1+xcex2)Ykxe2x88x920.5xcex2Yk+1xe2x80x83xe2x80x83(12)
fk(Xk+1)=xe2x88x920.5xcex2Yk+(1+xcex2)Yk+1xe2x88x920.5xcex2Yk+2xe2x80x83xe2x80x83(13)
{circle around (7)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the first-order differential coefficient of the spline interpolating function fkxe2x88x921 at the picture element Xk, as represented by Formula (4):
fkxe2x80x2(Xk)=fkxe2x88x921xe2x80x2(Xk)xe2x80x83xe2x80x83(4)
{circle around (8)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the first-order differential coefficient of the spline interpolating function fk+1 at the picture element Xk+1, as represented by Formula (5):
fkxe2x80x2(Xk+1)=fk+1xe2x80x2(Xk+1)xe2x80x83xe2x80x83(5)
{circle around (9)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk may coincide with the gradient of the original image signal components Ykxe2x88x921 and Yk+1 representing the picture elements Xkxe2x88x921 and Xk+1, which are located before and after the picture element Xk, as represented by Formula (14):
fkxe2x80x2(Xk)=(Yk+1xe2x88x92Ykxe2x88x921)/(Xk+1xe2x88x92Xkxe2x88x921)xe2x80x83xe2x80x83(14)
xe2x80x83and
{circle around (10)} the first-order differential coefficient of the spline interpolating function fk at the picture element Xk+1 may coincide with the gradient of the original image signal components Yk and Yk+2 representing the picture elements Xk and Xk+2, which are located before and after the picture element Xk+1, as represented by Formula (15):
fkxe2x80x2(Xk+1)=(Yk+2xe2x88x92Yk)/(Xk+2xe2x88x92Xk)xe2x80x83xe2x80x83(15)
c) calculating a mean value of the set of the interpolation coefficients akxe2x88x921 and bkxe2x88x921, a mean value of the set of the interpolation coefficients ak and bk, a mean value of the set of the interpolation coefficients ak+1 and bk+1, and a mean value of the set of the interpolation coefficients ak+2 and bk+2, which sets respectively correspond to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2, the calculated mean values being taken as the values of new interpolation coefficients ak+1, ak, ak+1, and ak+2, and
d) calculating the interpolated image signal component Yp corresponding to the interpolation point Xp in accordance with the calculated new interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, and the original image signal components Ykxe2x88x921, Yk, Yk+1 and Yk+2.
In the interpolating operation process described in (A) above, the calculated interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 may be respectively represented by Formulas (8), (9), (10), and (11):
akxe2x88x921=xe2x88x92(xcex1/2)t(txe2x88x921)2xe2x80x83xe2x80x83(8)
ak=(2xe2x88x92xcex1/2)t3xe2x88x92(3xe2x88x92xcex1/2)t2+1xe2x80x83xe2x80x83(9)
ak+1=(xcex1/2xe2x88x922)t3+(3xe2x88x92xcex1)t2+(xcex1/2)txe2x80x83xe2x80x83(10)
ak+2=(xcex1/2)t2(txe2x88x921)xe2x80x83xe2x80x83(11)
in which t, where 0xe2x89xa6t less than 1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1.
In the interpolating operation process described in (B) above, the calculated interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 may be respectively represented by Formulas (16), (17), (18), and (19):
                              a                      k            -            1                          =                                            -                              (                                  β                  +                                      1                    /                    2                                                  )                                      ⁢                          xe2x80x83                        ⁢                          t              3                                +                                    (                                                3                  ⁢                                      β                    /                    2                                                  +                1                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                -                                    (                              1                /                2                            )                        ⁢                          xe2x80x83                        ⁢            t                    -                      β            /            2                                              (        16        )                                          a          k                =                              3            ⁢                          (                              β                +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              3                                -                                    (                                                9                  ⁢                                      xe2x80x83                                    ⁢                                      β                    /                    2                                                  +                                  5                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                +          β          +          1                                    (        17        )                                          a                      k            +            1                          =                                            -              3                        ⁢                          (                              β                +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              3                                +                                    (                                                9                  ⁢                                      xe2x80x83                                    ⁢                                      β                    /                    2                                                  +                2                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                +                                    (                              1                /                2                            )                        ⁢                          xe2x80x83                        ⁢            t                    -                      β            /            2                                              (        18        )                                          a                      k            +            2                          =                                            (                              β                +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              3                                -                                    (                                                3                  ⁢                                      xe2x80x83                                    ⁢                                      β                    /                    2                                                  +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                                          (        19        )            
in which t, where 0xe2x89xa6t less than 1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1.
In the interpolating operation process described in (C) above, the calculated new interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which represent the mean values, may be respectively represented by Formulas (20), (21), (22), and (23):
                                                                        a                                  k                  -                  1                                            =                              xe2x80x83                            ⁢                                                                    -                                          {                                                                        (                                                      α                            +                                                          2                              ⁢                                                              xe2x80x83                                                            ⁢                              β                                                        +                            1                                                    )                                                /                        4                                            }                                                        ⁢                                      xe2x80x83                                    ⁢                                      t                    3                                                  +                                                      {                                                                  (                                                                              2                            ⁢                                                          xe2x80x83                                                        ⁢                            α                                                    +                                                      3                            ⁢                                                          xe2x80x83                                                        ⁢                            β                                                    +                          2                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                                      t                    2                                                  -                                                                                                        xe2x80x83                            ⁢                                                                    {                                                                  (                                                  α                          +                          1                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                  t                                -                                  β                  /                  4                                                                                        (        20        )                                          a          k                =                                            {                                                (                                                            -                      α                                        +                                          6                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    7                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              3                                +                                    {                                                (                                      α                    -                                          9                      ⁢                                              xe2x80x83                                            ⁢                      β                                        -                    11                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              2                                +                      β            /            2                    +          1                                    (        21        )                                                                                    a                                  k                  +                  1                                            =                              xe2x80x83                            ⁢                                                                    {                                                                  (                                                  α                          -                                                      6                            ⁢                                                          xe2x80x83                                                        ⁢                            β                                                    -                          7                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                                      t                    3                                                  +                                                      {                                                                  (                                                                                                            -                              2                                                        ⁢                                                          xe2x80x83                                                        ⁢                            α                                                    +                                                      9                            ⁢                                                          xe2x80x83                                                        ⁢                            β                                                    +                          10                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                                      t                    2                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    {                                                                  (                                                  α                          +                          1                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                  t                                -                                  β                  /                  4                                                                                        (        22        )                                          a                      k            +            2                          =                                            {                                                (                                      α                    +                                          2                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    1                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              3                                -                                    {                                                (                                      α                    +                                          3                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    1                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              2                                                          (        23        )            
in which t, where 0xe2x89xa6t less than 1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1.
The present invention also provides an apparatus for carrying out the interpolating operation method for an image signal in accordance with the present invention. Specifically, the present invention also provides an interpolating operation apparatus for an image signal, wherein an interpolated image signal component corresponding to an interpolation point is calculated from original image signal components of an original image signal representing an original image, which represent a plurality of sampling points arrayed at predetermined intervals and in a lattice-like form, the apparatus comprising:
i) an edge presence or absence judging means for making a judgment as to whether the interpolation point belongs to an image edge portion, at which the change in the original image signal is sharp, or belongs to a flat portion, at which the change in the original image signal is unsharp,
ii) a first interpolating operation means for calculating an interpolated image signal component corresponding to an interpolation point, which belongs to the image edge portion,
iii) a second interpolating operation means for calculating an interpolated image signal component corresponding to an interpolation point, which belongs to the flat portion, and
iv) an operation change-over means for changing the first interpolating operation means and the second interpolating operation means over to each other, such that the first interpolating operation means may be utilized in cases where, as a result of the judgment made by the edge presence or absence judging means, it has been judged that the interpolation point belongs to the image edge portion, and such that the second interpolating operation means may be utilized in cases where, as a result of the judgment made by the edge presence or absence judging means, it has been judged that the interpolation point belongs to the flat portion.
By way of example, as the first interpolating operation means, the first interpolating operation means described in (1) or (2) below may be employed.
(1) A first interpolating operation means comprising:
a) an edge extending direction specifying means for specifying the direction, along which the image edge portion extends, with respect to the array directions of the sampling points in a unit lattice,
b) a first operation means comprising:
a region dividing means for dividing the unit lattice into two triangular regions with the image edge portion serving as the boundary therebetween, the image edge portion extending along an oblique direction with respect to the array directions of the sampling points in the unit lattice,
a region selecting means for selecting a triangular region, which contains the interpolation point therein, from the two triangular regions, and
an operation means for calculating the interpolated image signal component corresponding to the interpolation point, the calculation being made from the original image signal components, which represent the three sampling points, that constitute the triangular region containing the interpolation point therein,
c) a second operation means for calculating the interpolated image signal component corresponding to the interpolation point, the calculation being made from the original image signal components, which represent the four sampling points, that constitute the unit lattice containing the interpolation point therein, and
d) an operation selecting means for:
selecting the first operation means in cases where, as a result of the specifying carried out by the edge extending direction specifying means, it has been specified that the image edge portion extends along an oblique direction with respect to the array directions of the sampling points in the unit lattice, and
selecting the second operation means in cases where, as a result of the specifying carried out by the edge extending direction specifying means, it has been specified that the image edge portion extends along a direction parallel to one of the array directions of the sampling points in the unit lattice.
(2) A first interpolating operation means comprising:
a) an interpolation coefficient calculating means for calculating each of interpolation coefficients, by which the corresponding one of the original image signal components is to be multiplied, from the original image signal components, which represent a plurality of the sampling points located in the vicinity of the interpolation point,
b) an image density gradient vector calculating means for calculating an image density gradient vector at the interpolation point on the original image, which is represented by the original image signal components,
c) a distance calculating means for calculating the distance between a line segment, which intersects perpendicularly to the image density gradient vector, and each of the sampling points located in the vicinity of the interpolation point,
d) a correction means for correcting the interpolation coefficients such that the interpolation coefficient, by which the corresponding original image signal component is to be multiplied, may become small for a sampling point, for which the image density gradient vector and/or the distance is comparatively large, and
e) an operation processing means for multiplying the original image signal component by the corresponding interpolation coefficient, which has been corrected by the correction means.
In cases where the first interpolating operation means described in (1) above is employed, the edge extending direction specifying means may specify the direction, along which the image edge portion extends, by, for example:
(a) grouping each of two sets of sampling points, each set being constituted of two sampling points, which are located at two diagonal positions facing each other in the unit lattice, that contains the interpolation point therein,
calculating the difference between the original image signal components representing the two sampling points, which constitute each of the two sets of sampling points, and
comparing the differences, which have been calculated for the two sets of sampling points, with each other; or
(b) grouping each of two sets of sampling points, each set being constituted of two sampling points, which are located at two diagonal positions facing each other in the unit lattice, that contains the interpolation point therein,
calculating the difference between the original image signal components representing the two sampling points, which constitute each of the two sets of sampling points,
comparing the differences, which have been calculated for the two sets of sampling points, with each other, and
carrying out an operation in accordance with the original image signal components representing the sampling points, which are located around the unit lattice, that contains the interpolation point therein; or
(c) calculating an image density gradient vector with respect to each of the two array directions of the sampling points in the unit lattice, the calculation being made from the original image signal components representing four sampling points, which constitute the unit lattice, that contains the interpolation point therein, and
making a judgment from the magnitude and the product of the two image density gradient vectors, which have been calculated with respect to the two array directions of the sampling points in the unit lattice.
Regardless of the constitution of the first interpolating operation means, the second interpolating operation means may comprise:
an input means for inputting an instruction concerning the alteration of sharpness of the flat portion from the exterior, and
an interpolating operation means, with which the sharpness of the flat portion is capable of being altered in accordance with the instruction inputted from the input means.
By way of example, the interpolating operation means, with which the sharpness of the flat portion is capable of being altered, may be:
(I) a spline interpolating operation means, or
(II) an interpolating operation means for:
linearly combining interpolation coefficients Bij and Cij, which correspond to each other and are set for each of the original image signal components Yij, in two different interpolating functions f and g (for example, a cubic spline interpolating operation function and a B spline interpolating operation function) for obtaining two interpolation images having different levels of sharpness, which functions are represented by Formulas (24) and (25), the linear combination being carried out with Formula (26), a new interpolation coefficient Aij being obtained from the linear combination, and
carrying out an interpolating operation on the original image signal components Yij by using an interpolating function h having the new interpolation coefficient Aij, which function is represented by Formula (27), an interpolation image signal being obtained from the interpolating operation, the interpolation image signal being made up of a series of image signal components, which occur at intervals different from those of the original image signal components Yij:
f=xcexa3Bijxc2x7Yijxe2x80x83xe2x80x83(24)
g=xcexa3Cijxc2x7Yijxe2x80x83xe2x80x83(25)
Aij=(1xe2x88x92xcex1)Bij+xcex1Cijxe2x80x83xe2x80x83(26)
h=xcexa3Aijxc2x7Yijxe2x80x83xe2x80x83(27)
xe2x80x83in which i=1, 2, . . . , j=1, 2, . . . , and
xcex1 represents one of all real numbers.
As the spline interpolating operation means described in (I) above, by way of example, one of the interpolating operation means described in (A), (B), and (C) below may be employed.
(A) The spline interpolating operation means is an interpolating operation means for obtaining an interpolated image signal component with Formula (1),
Yp=akxe2x88x921Ykxe2x88x921+akYk+ak+1Yk+1+ak+2Yk+2xe2x80x83xe2x80x83(1)
in which Ykxe2x88x921, Yk, Yk+1, and Yk+2 represent the original image signal components representing picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and akxe2x88x921, ak, ak+1, and ak+2 represent the interpolation coefficients,
the spline interpolating operation means comprising:
1) a storage means for storing information representing the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which respectively correspond to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2 representing the picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, and which are set to be respectively represented by Formulas (8), (9), (10), and (11):
akxe2x88x921=xe2x88x92(xcex1/2)t(txe2x88x921)2xe2x80x83xe2x80x83(8)
ak=(2xe2x88x92xcex1/2)t3xe2x88x92(3xe2x88x92xcex1/2)t2+1xe2x80x83xe2x80x83(9)
ak+1=(xcex1/2xe2x88x922)t3+(3xe2x88x92xcex1)t2+(xcex1/2)txe2x80x83xe2x80x83(10)
ak+2=(xcex1/2)t2(txe2x88x921)xe2x80x83xe2x80x83(11)
xe2x80x83in which xcex1 represents the parameter determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation, and t, where 0xe2x89xa6t less than 1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1,
2) an input means for inputting the arbitrary parameter xcex1, which determines the sharpness of the secondary image reproduced from the interpolation image signal obtained from the interpolating operation,
3) an interpolation coefficient operation means for calculating the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 in accordance with the parameter xcex1, the calculation being carried out from the interpolation coefficients, which are stored in the storage means, and the parameter xcex1 inputted from the input means, and
4) an interpolating operation means for storing Formula (1) as the operation formula, and calculating the value of the interpolated image signal component Yp, which corresponds to the interpolation point Xp, with Formula (1) in accordance with the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which have been calculated by the interpolation coefficient operation means, and the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2.
(B) The spline interpolating operation means is an interpolating operation means for obtaining an interpolated image signal component with Formula (1),
Yp=akxe2x88x921Ykxe2x88x921+akYk+ak+1Yk+1+ak+2Yk+2xe2x80x83xe2x80x83(1)
in which Ykxe2x88x921, Yk, Y+1, and Yk+2 represent the original image signal components representing picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and akxe2x88x921, ak, ak+1, and ak+2 represent the interpolation coefficients,
the spline interpolating operation means comprising:
1) a storage means for storing information representing the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which respectively correspond to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2 representing the picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, and which are set to be respectively represented by Formulas (16), (17), (18), and (19):
                              a                      k            -            1                          =                                            -                              (                                  β                  +                                      1                    /                    2                                                  )                                      ⁢                          xe2x80x83                        ⁢                          t              3                                +                                    (                                                3                  ⁢                                      β                    /                    2                                                  +                1                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                -                                    (                              1                /                2                            )                        ⁢                          xe2x80x83                        ⁢            t                    -                      β            /            2                                              (        16        )                                          a          k                =                              3            ⁢                          (                              β                +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              3                                -                                    (                                                9                  ⁢                                      xe2x80x83                                    ⁢                                      β                    /                    2                                                  +                                  5                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                +          β          +          1                                    (        17        )                                          a                      k            +            1                          =                                            -              3                        ⁢                          (                              β                +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              3                                +                                    (                                                9                  ⁢                                      xe2x80x83                                    ⁢                                      β                    /                    2                                                  +                2                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                +                                    (                              1                /                2                            )                        ⁢                          xe2x80x83                        ⁢            t                    -                      β            /            2                                              (        18        )                                          a                      k            +            2                          =                                            (                              β                +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              3                                -                                    (                                                3                  ⁢                                      xe2x80x83                                    ⁢                                      β                    /                    2                                                  +                                  1                  /                  2                                            )                        ⁢                          xe2x80x83                        ⁢                          t              2                                                          (        19        )            
xe2x80x83in which xcex2 represents the parameter determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation, and t, where 0xe2x89xa6t less than 1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1,
2) an input means for inputting the arbitrary parameter xcex2, which determines the sharpness of the secondary image reproduced from the interpolation image signal obtained from the interpolating operation,
3) an interpolation coefficient operation means for calculating the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 in accordance with the parameter xcex2, the calculation being carried out from the interpolation coefficients, which are stored in the storage means, and the parameter xcex2 inputted from the input means, and
4) an interpolating operation means for storing Formula (1) as the operation formula, and calculating the value of the interpolated image signal component Yp, which corresponds to the interpolation point Xp, with Formula (1) in accordance with the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which have been calculated by the interpolation coefficient operation means, and the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2.
(C) The spline interpolating operation means is an interpolating operation means for obtaining an interpolated image signal component with Formula (1),
Yp=akxe2x88x921Ykxe2x88x921+akYk+ak+1Yk+1+ak+2Yk+2xe2x80x83xe2x80x83(1)
in which Ykxe2x88x921, Yk, Yk+1, and Yk+2 represent the original image signal components representing picture elements Xkxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, Yp represents the interpolated image signal component corresponding to an interpolation point Xp located between the picture elements Xk and Xk+1, and akxe2x88x921, ak, ak+1, and ak+2 represent the interpolation coefficients,
the spline interpolating operation means comprising:
1) a storage means for storing information representing the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which respectively correspond to the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2 representing the picture elements Ykxe2x88x921, Xk, Xk+1, and Xk+2 in the original image, and which are set to be respectively represented by Formulas (20), (21), (22), and (23):
                                                                        a                                  k                  -                  1                                            =                              xe2x80x83                            ⁢                                                                    -                                          {                                                                        (                                                      α                            +                                                          2                              ⁢                                                              xe2x80x83                                                            ⁢                              β                                                        +                            1                                                    )                                                /                        4                                            }                                                        ⁢                                      xe2x80x83                                    ⁢                                      t                    3                                                  +                                                      {                                                                  (                                                                              2                            ⁢                                                          xe2x80x83                                                        ⁢                            α                                                    +                                                      3                            ⁢                                                          xe2x80x83                                                        ⁢                            β                                                    +                          2                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                                      t                    2                                                  -                                                                                                        xe2x80x83                            ⁢                                                                    {                                                                  (                                                  α                          +                          1                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                  t                                -                                  β                  /                  4                                                                                        (        20        )                                          a          k                =                                            {                                                (                                                            -                      α                                        +                                          6                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    7                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              3                                +                                    {                                                (                                      α                    -                                          9                      ⁢                                              xe2x80x83                                            ⁢                      β                                        -                    11                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              2                                +                      β            /            2                    +          1                                    (        21        )                                                                                    a                                  k                  +                  1                                            =                              xe2x80x83                            ⁢                                                                    {                                                                  (                                                  α                          -                                                      6                            ⁢                                                          xe2x80x83                                                        ⁢                            β                                                    -                          7                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                                      t                    3                                                  +                                                      {                                                                  (                                                                                                            -                              2                                                        ⁢                                                          xe2x80x83                                                        ⁢                            α                                                    +                                                      9                            ⁢                                                          xe2x80x83                                                        ⁢                            β                                                    +                          10                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                                      t                    2                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    {                                                                  (                                                  α                          +                          1                                                )                                            /                      4                                        }                                    ⁢                                      xe2x80x83                                    ⁢                  t                                -                                  β                  /                  4                                                                                        (        22        )                                          a                      k            +            2                          =                                            {                                                (                                      α                    +                                          2                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    1                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              3                                -                                    {                                                (                                      α                    +                                          3                      ⁢                                              xe2x80x83                                            ⁢                      β                                        +                    1                                    )                                /                4                            }                        ⁢                          xe2x80x83                        ⁢                          t              2                                                          (        23        )            
xe2x80x83in which xcex1 and xcex2 represent the parameters determining the sharpness of a secondary image represented by the interpolation image signal obtained from the interpolating operation, and t, where 0xe2x89xa6t less than 1, represents the position of the interpolation point Xp, the position being taken with respect to the picture element Xk, that serves as a reference position, and in the direction heading toward the picture element Xk+1, the lattice interval of the original image signal components being set to be equal to 1,
2) an input means for inputting the arbitrary parameters xcex1 and xcex2, which determine the sharpness of the secondary image reproduced from the interpolation image signal obtained from the interpolating operation,
3) an interpolation coefficient operation means for calculating the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2 in accordance with the parameters xcex1 and xcex2, the calculation being carried out from the interpolation coefficients, which are stored in the storage means, and the parameters xcex1 and xcex2 inputted from the input means, and
4) an interpolating operation means for storing Formula (1) as the operation formula, and calculating the value of the interpolated image signal component Yp, which corresponds to the interpolation point Xp, with Formula (1) in accordance with the interpolation coefficients akxe2x88x921, ak, ak+1, and ak+2, which have been calculated by the interpolation coefficient operation means, and the original image signal components Ykxe2x88x921, Yk, Yk+1, and Yk+2.
The interpolating operation method and apparatus for an image signal in accordance with the present invention have the advantages described below over the conventional interpolating operation method and apparatus, wherein the same interpolating operation process is employed regardless of whether an interpolation point is located at an image edge portion, a flat portion, or the like, in the image. Specifically, the interpolating operation processes, one of which is to be employed for the interpolation point, are changed over to each other in accordance with whether the interpolation point is located at the image edge portion or the flat portion in the image. The interpolating operation process, which is suitable for the image edge portion, is employed for the interpolation point located at the image edge portion. Also, the interpolating operation process, which is suitable for the flat portion, is employed for the interpolation point located at the flat portion. In this manner, a reproduced visible image, which has good image quality as a whole and can serve as an effective tool in, particularly, the accurate and efficient diagnosis of an illness, can be obtained from the interpolation image signal, which has been obtained from the interpolating operation.
For example, in cases where it has been judged that the interpolation point belongs to the image edge portion, the direction, along which the image edge portion extends, is discriminated (i.e., specified). In cases where it has been specified that the image edge portion extends along an oblique direction with respect to the array directions of the sampling points in the unit lattice, the unit lattice is divided into two triangular regions with the image edge portion serving as the boundary between them. Also, the triangular region, which contains the interpolation point therein, is selected from the two triangular regions. The interpolated image signal component corresponding to the interpolation point is calculated from the original image signal components, which represent the three lattice points (i.e., the three sampling points), that constitute the triangular region containing the interpolation point therein. Therefore, the interpolated image signal component corresponding to the interpolation point, which is located at the oblique image edge portion, does not depend upon the original image signal components, which represent the picture elements having markedly different image density values (or luminance values or other kinds of signal values). Accordingly, the problems can be prevented from occurring in that an interpolated point having an intermediate level of image density occurs in a high image density region or a low image density region.
In cases where it has been judged that the interpolation point belongs to the image edge portion, and it has been specified that the image edge portion extends along a direction parallel (or perpendicular) to one of the array directions of the sampling points in the unit lattice, the interpolated image signal component corresponding to the interpolation point is calculated from the original image signal components, which represent the four lattice points (i.e., the four sampling points), that constitute the unit lattice containing the interpolation point therein. In such cases, the calculation of the interpolated image signal component corresponding to the interpolation point, which is located at the image edge portion extending along the direction parallel (or perpendicular) to one of the array directions of the sampling points in the unit lattice, may be carried out by using the same operation process as the conventional one.
In the interpolating operation method and apparatus for an image signal in accordance with the present invention, in cases where it has been judged that the interpolation point belongs to the image edge portion, the image density gradient vector at the interpolation point may be calculated. Also, the distance between the line segment, which intersects perpendicularly to the image density gradient vector, and each of the sampling points, which are located in the vicinity of the interpolation point, may be calculated. The interpolation coefficients may then be corrected such that the interpolation coefficient, by which the original image signal component representing a sampling point is to be multiplied, may become small for the sampling point, for which the image density gradient vector and/or the distance is comparatively large. With the interpolating operation method and apparatus for an image signal in accordance with the present invention, which are constituted in this manner, when the original image signal components representing the sampling points, which are located at positions remote from the line segment (i.e., the image edge portion), are used in the interpolating operation, the degrees of contribution of the original image signal components to the interpolating operation can be kept low. As a result, the degrees of contribution of the original image signal components representing the sampling points, which are located at positions in the vicinity of the image edge portion, i.e. at positions along the image edge portion, to the interpolating operation can be kept relatively high. Therefore, an approximately the same level of image density value (interpolated image signal component) as the image density values of the image edge portion is assigned to the interpolation point, which is located at the image edge portion. Accordingly, the step-like pattern in the original image is not enlarged. Even if the image size is enlarged, the problems can be prevented from occurring in that the step-like pattern at the image edge portion, which extends in the oblique direction, is enlarged.
In cases where it has been judged that the interpolation point belongs to the flat portion in the original image, the interpolating operation process enabling the sharpness to be adjusted, such as the spline interpolating operation process or the interpolating operation process, which comprises the combination of the cubic spline interpolating operation and the third-order B spline interpolating operation, may be carried out by taking the four lattice points (i.e., the four sampling points), that constitute the unit lattice containing the interpolation point therein, as reference and by also using the original image signal components, which represents the sampling points located around the unit lattice. In this manner, the sharpness of the flat portion in the image can be adjusted freely, and a reproduced visible image, which has good image quality and can serve as an effective tool in, particularly, the accurate and efficient diagnosis of an illness, can be obtained.